# Homework Help: How do I know if this field has a mass term?

1. Sep 17, 2007

### Lecticia

1. Special Relativity

2. The problem statement, all variables and given/known data
Consider this Lagrangian:

L=(1/2) (\partial_{\mu} \Psi)(\partial^{mu} \Psi) + \exp(-(a\times \Psi)^2)

Have this field a mass term?

2. Relevant equations

3. The attempt at a solution

2. Sep 17, 2007

### Astronuc

Staff Emeritus
Is this what one intended to write, or is this given in some text?

$$L= \frac{1}{2} (\partial_{\mu} \Psi)(\partial^{\mu} \Psi) + e^{-{(a \Psi)}^2}$$

3. Sep 17, 2007

### Lecticia

Yes, exactly this Lagrangian, where \Psi is a scalar field.

Last edited: Sep 17, 2007
4. Sep 17, 2007

### nrqed

This is a nonlinear field theory so, strictly speaking, there is no clear meaning for a mass term.
But I am guessing that they want you to treat the parameter "a" as small and to do a Taylor expansion of the exponential. If you do that, you will generate a mass term.

That's my guess.

5. Sep 17, 2007

### dextercioby

Well, just one question, you have the lagrangian, what are the field eqn's ?

6. Sep 17, 2007

### Lecticia

Do you mean the motion equations?

7. Sep 17, 2007